<!DOCTYPE html>
<html lang="zh-CN">
<head>
  <meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1, maximum-scale=2">
<meta name="theme-color" content="#222">
<meta name="generator" content="Hexo 5.4.2">
  <link rel="apple-touch-icon" sizes="180x180" href="/images/apple-touch-icon-next.png">
  <link rel="icon" type="image/png" sizes="32x32" href="/images/favicon-32x32-next.png">
  <link rel="icon" type="image/png" sizes="16x16" href="/images/favicon-16x16-next.png">
  <link rel="mask-icon" href="/images/logo.svg" color="#222">

<link rel="stylesheet" href="/css/main.css">


<link rel="stylesheet" href="/lib/font-awesome/css/all.min.css">

<script id="hexo-configurations">
    var NexT = window.NexT || {};
    var CONFIG = {"hostname":"wrr123.github.io","root":"/","scheme":"Muse","version":"7.8.0","exturl":false,"sidebar":{"position":"left","display":"post","padding":18,"offset":12,"onmobile":false},"copycode":{"enable":false,"show_result":false,"style":null},"back2top":{"enable":true,"sidebar":false,"scrollpercent":false},"bookmark":{"enable":false,"color":"#222","save":"auto"},"fancybox":false,"mediumzoom":false,"lazyload":false,"pangu":false,"comments":{"style":"tabs","active":null,"storage":true,"lazyload":false,"nav":null},"algolia":{"hits":{"per_page":10},"labels":{"input_placeholder":"Search for Posts","hits_empty":"We didn't find any results for the search: ${query}","hits_stats":"${hits} results found in ${time} ms"}},"localsearch":{"enable":true,"trigger":"auto","top_n_per_article":1,"unescape":false,"preload":false},"motion":{"enable":true,"async":false,"transition":{"post_block":"fadeIn","post_header":"slideDownIn","post_body":"slideDownIn","coll_header":"slideLeftIn","sidebar":"slideUpIn"}},"path":"search.json"};
  </script>

  <meta name="description" content="Oracle建立索引的目的是为了避免全表扫描，提高查询的效率。">
<meta property="og:type" content="article">
<meta property="og:title" content="oracle中不走索引的一些情况">
<meta property="og:url" content="https://wrr123.github.io/2021/07/26/oracle%E4%B8%AD%E4%B8%8D%E8%B5%B0%E7%B4%A2%E5%BC%95%E7%9A%84%E4%B8%80%E4%BA%9B%E6%83%85%E5%86%B5/index.html">
<meta property="og:site_name" content="一缕烟气">
<meta property="og:description" content="Oracle建立索引的目的是为了避免全表扫描，提高查询的效率。">
<meta property="og:locale" content="zh_CN">
<meta property="article:published_time" content="2021-07-26T08:22:41.000Z">
<meta property="article:modified_time" content="2022-02-18T02:52:04.496Z">
<meta property="article:author" content="田园隐士">
<meta name="twitter:card" content="summary">

<link rel="canonical" href="https://wrr123.github.io/2021/07/26/oracle%E4%B8%AD%E4%B8%8D%E8%B5%B0%E7%B4%A2%E5%BC%95%E7%9A%84%E4%B8%80%E4%BA%9B%E6%83%85%E5%86%B5/">


<script id="page-configurations">
  // https://hexo.io/docs/variables.html
  CONFIG.page = {
    sidebar: "",
    isHome : false,
    isPost : true,
    lang   : 'zh-CN'
  };
</script>

  <title>oracle中不走索引的一些情况 | 一缕烟气</title>
  






  <noscript>
  <style>
  .use-motion .brand,
  .use-motion .menu-item,
  .sidebar-inner,
  .use-motion .post-block,
  .use-motion .pagination,
  .use-motion .comments,
  .use-motion .post-header,
  .use-motion .post-body,
  .use-motion .collection-header { opacity: initial; }

  .use-motion .site-title,
  .use-motion .site-subtitle {
    opacity: initial;
    top: initial;
  }

  .use-motion .logo-line-before i { left: initial; }
  .use-motion .logo-line-after i { right: initial; }
  </style>
</noscript>

<style>mjx-container[jax="SVG"] {
  direction: ltr;
}

mjx-container[jax="SVG"] > svg {
  overflow: visible;
}

mjx-container[jax="SVG"][display="true"] {
  display: block;
  text-align: center;
  margin: 1em 0;
}

mjx-container[jax="SVG"][justify="left"] {
  text-align: left;
}

mjx-container[jax="SVG"][justify="right"] {
  text-align: right;
}

g[data-mml-node="merror"] > g {
  fill: red;
  stroke: red;
}

g[data-mml-node="merror"] > rect[data-background] {
  fill: yellow;
  stroke: none;
}

g[data-mml-node="mtable"] > line[data-line] {
  stroke-width: 70px;
  fill: none;
}

g[data-mml-node="mtable"] > rect[data-frame] {
  stroke-width: 70px;
  fill: none;
}

g[data-mml-node="mtable"] > .mjx-dashed {
  stroke-dasharray: 140;
}

g[data-mml-node="mtable"] > .mjx-dotted {
  stroke-linecap: round;
  stroke-dasharray: 0,140;
}

g[data-mml-node="mtable"] > svg {
  overflow: visible;
}

[jax="SVG"] mjx-tool {
  display: inline-block;
  position: relative;
  width: 0;
  height: 0;
}

[jax="SVG"] mjx-tool > mjx-tip {
  position: absolute;
  top: 0;
  left: 0;
}

mjx-tool > mjx-tip {
  display: inline-block;
  padding: .2em;
  border: 1px solid #888;
  font-size: 70%;
  background-color: #F8F8F8;
  color: black;
  box-shadow: 2px 2px 5px #AAAAAA;
}

g[data-mml-node="maction"][data-toggle] {
  cursor: pointer;
}

mjx-status {
  display: block;
  position: fixed;
  left: 1em;
  bottom: 1em;
  min-width: 25%;
  padding: .2em .4em;
  border: 1px solid #888;
  font-size: 90%;
  background-color: #F8F8F8;
  color: black;
}

foreignObject[data-mjx-xml] {
  font-family: initial;
  line-height: normal;
  overflow: visible;
}

.MathJax path {
  stroke-width: 3;
}

mjx-container[display="true"] {
  overflow: auto hidden;
}

mjx-container[display="true"] + br {
  display: none;
}
</style><link rel="alternate" href="/atom.xml" title="一缕烟气" type="application/atom+xml">
</head>

<body itemscope itemtype="http://schema.org/WebPage">
  <div class="container use-motion">
    <div class="headband"></div>

    <header class="header" itemscope itemtype="http://schema.org/WPHeader">
      <div class="header-inner"><div class="site-brand-container">
  <div class="site-nav-toggle">
    <div class="toggle" aria-label="切换导航栏">
      <span class="toggle-line toggle-line-first"></span>
      <span class="toggle-line toggle-line-middle"></span>
      <span class="toggle-line toggle-line-last"></span>
    </div>
  </div>

  <div class="site-meta">

    <a href="/" class="brand" rel="start">
      <span class="logo-line-before"><i></i></span>
      <h1 class="site-title">一缕烟气</h1>
      <span class="logo-line-after"><i></i></span>
    </a>
      <p class="site-subtitle" itemprop="description">沧海月明珠有泪，蓝田日暖玉生烟</p>
  </div>

  <div class="site-nav-right">
    <div class="toggle popup-trigger">
        <i class="fa fa-search fa-fw fa-lg"></i>
    </div>
  </div>
</div>




<nav class="site-nav">
  <ul id="menu" class="main-menu menu">
        <li class="menu-item menu-item-home">

    <a href="/" rel="section"><i class="fa fa-home fa-fw"></i>首页</a>

  </li>
        <li class="menu-item menu-item-archives">

    <a href="/archives/" rel="section"><i class="fa fa-archive fa-fw"></i>归档</a>

  </li>
      <li class="menu-item menu-item-search">
        <a role="button" class="popup-trigger"><i class="fa fa-search fa-fw"></i>搜索
        </a>
      </li>
  </ul>
</nav>



  <div class="search-pop-overlay">
    <div class="popup search-popup">
        <div class="search-header">
  <span class="search-icon">
    <i class="fa fa-search"></i>
  </span>
  <div class="search-input-container">
    <input autocomplete="off" autocapitalize="off"
           placeholder="搜索..." spellcheck="false"
           type="search" class="search-input">
  </div>
  <span class="popup-btn-close">
    <i class="fa fa-times-circle"></i>
  </span>
</div>
<div id="search-result">
  <div id="no-result">
    <i class="fa fa-spinner fa-pulse fa-5x fa-fw"></i>
  </div>
</div>

    </div>
  </div>

</div>
    </header>

    
  <div class="back-to-top">
    <i class="fa fa-arrow-up"></i>
    <span>0%</span>
  </div>


    <main class="main">
      <div class="main-inner">
        <div class="content-wrap">
          

          <div class="content post posts-expand">
            

    
  
  
  <article itemscope itemtype="http://schema.org/Article" class="post-block" lang="zh-CN">
    <link itemprop="mainEntityOfPage" href="https://wrr123.github.io/2021/07/26/oracle%E4%B8%AD%E4%B8%8D%E8%B5%B0%E7%B4%A2%E5%BC%95%E7%9A%84%E4%B8%80%E4%BA%9B%E6%83%85%E5%86%B5/">

    <span hidden itemprop="author" itemscope itemtype="http://schema.org/Person">
      <meta itemprop="image" content="/images/avatar.gif">
      <meta itemprop="name" content="田园隐士">
      <meta itemprop="description" content="talk is cheap, show me the code">
    </span>

    <span hidden itemprop="publisher" itemscope itemtype="http://schema.org/Organization">
      <meta itemprop="name" content="一缕烟气">
    </span>
      <header class="post-header">
        <h1 class="post-title" itemprop="name headline">
          oracle中不走索引的一些情况
        </h1>

        <div class="post-meta">
            <span class="post-meta-item">
              <span class="post-meta-item-icon">
                <i class="far fa-calendar"></i>
              </span>
              <span class="post-meta-item-text">发表于</span>

              <time title="创建时间：2021-07-26 16:22:41" itemprop="dateCreated datePublished" datetime="2021-07-26T16:22:41+08:00">2021-07-26</time>
            </span>
              <span class="post-meta-item">
                <span class="post-meta-item-icon">
                  <i class="far fa-calendar-check"></i>
                </span>
                <span class="post-meta-item-text">更新于</span>
                <time title="修改时间：2022-02-18 10:52:04" itemprop="dateModified" datetime="2022-02-18T10:52:04+08:00">2022-02-18</time>
              </span>

          
            <span class="post-meta-item" title="阅读次数" id="busuanzi_container_page_pv" style="display: none;">
              <span class="post-meta-item-icon">
                <i class="fa fa-eye"></i>
              </span>
              <span class="post-meta-item-text">阅读次数：</span>
              <span id="busuanzi_value_page_pv"></span>
            </span><br>
            <span class="post-meta-item" title="本文字数">
              <span class="post-meta-item-icon">
                <i class="far fa-file-word"></i>
              </span>
                <span class="post-meta-item-text">本文字数：</span>
              <span>1.5k</span>
            </span>
            <span class="post-meta-item" title="阅读时长">
              <span class="post-meta-item-icon">
                <i class="far fa-clock"></i>
              </span>
                <span class="post-meta-item-text">阅读时长 &asymp;</span>
              <span>1 分钟</span>
            </span>

        </div>
      </header>

    
    
    
    <div class="post-body" itemprop="articleBody">

      
        <p><div style="color:Chocolate;text-align:center;display:inline-block;width:100%;">
  Oracle建立索引的目的是为了避免全表扫描，提高查询的效率。
</div><br><span id="more"></span></p>
<h2 id="引子"><a href="#引子" class="headerlink" title="引子"></a>引子</h2><p>  有些情况下，即使建立了索引，但是执行写出来的查询还是很慢，然后通过执行计划发现是索引失效导致的（不走索引，走全表扫描）。</p>
<h2 id="在写sql的层面上，一些导致索引失效的骚操作"><a href="#在写sql的层面上，一些导致索引失效的骚操作" class="headerlink" title="在写sql的层面上，一些导致索引失效的骚操作"></a>在写sql的层面上，一些导致索引失效的骚操作</h2><ol>
<li><p>没有写where子句或查询条件没有建立索引</p>
</li>
<li><p>where子句上没有使用索引中的引导列</p>
<p>要使用索引，则查询条件中必须包含索引中的引导列。比如一个复合索引包含A, B, C, D四列，则A为引导列（排在第一位置的列）。如果where子句中所包含的列是BCD或者BD等情况，则只能使用非匹配索引扫描。</p>
<figure class="highlight sql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">-- 创建包含A，B，C，D四列的复合索引</span></span><br><span class="line"><span class="keyword">CREATE</span> INDEX INDEX_ABCD <span class="keyword">ON</span> LETTERS(A, B, C, D);</span><br><span class="line"><span class="comment">-- 下列语句不会使用复合索引</span></span><br><span class="line"><span class="keyword">SELECT</span> <span class="operator">*</span> <span class="keyword">FROM</span> LETTERS <span class="keyword">WHERE</span> B <span class="operator">=</span> <span class="string">'b'</span> <span class="keyword">AND</span> C <span class="operator">=</span> <span class="string">'c'</span>;</span><br><span class="line"><span class="keyword">SELECT</span> <span class="operator">*</span> <span class="keyword">FROM</span> LETTERS <span class="keyword">WHERE</span> B <span class="operator">=</span> <span class="string">'b'</span> <span class="keyword">AND</span> D <span class="operator">=</span> <span class="string">'d'</span>;</span><br><span class="line"><span class="keyword">SELECT</span> <span class="operator">*</span> <span class="keyword">FROM</span> LETTERS <span class="keyword">WHERE</span> C <span class="operator">=</span> <span class="string">'c'</span> <span class="keyword">AND</span> D <span class="operator">=</span> <span class="string">'d'</span>;</span><br><span class="line"><span class="keyword">SELECT</span> <span class="operator">*</span> <span class="keyword">FROM</span> LETTERS <span class="keyword">WHERE</span> B <span class="operator">=</span> <span class="string">'b'</span> <span class="keyword">AND</span> C <span class="operator">=</span> <span class="string">'c'</span> <span class="keyword">AND</span> D <span class="operator">=</span> <span class="string">'d'</span>;</span><br></pre></td></tr></table></figure>
</li>
<li><p>单独引用复合索引里排第一位置的索引列也会导致索引失效，复合索引必须复合使用才能生效。</p>
<figure class="highlight sql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">-- 单独使用复合索引中的引导列也不会触发复合索引</span></span><br><span class="line"><span class="keyword">SELECT</span> <span class="operator">*</span> <span class="keyword">FROM</span> LETTERS <span class="keyword">WHERE</span> A <span class="operator">=</span> <span class="string">'a'</span></span><br></pre></td></tr></table></figure>
</li>
<li><p>where子句中使用<code>is null</code>或者<code>is not null</code>。</p>
</li>
<li><p>where子句中使用函数</p>
<p>如果没有使用基于函数的索引，那么where子句中对存在索引有列使用函数时，会使优化器忽略这些索引。</p>
<figure class="highlight sql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">-- 在没有建立基于函数索引的字段上使用了函数，会导致索引失效</span></span><br><span class="line"><span class="keyword">SELECT</span> <span class="operator">*</span> <span class="keyword">FROM</span> STUFF <span class="keyword">WHERE</span> TRUNC(BIRTHDAY) <span class="operator">=</span> <span class="string">'2019-04-01'</span></span><br></pre></td></tr></table></figure>
<p>非要这样的话可以通过在索引上建立基于函数的索引来解决问题。</p>
<figure class="highlight sql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">-- 给BIRTHDAY列创建TRUNC函数的函数索引</span></span><br><span class="line"><span class="keyword">CREATE</span> INDEX STUFF_BIRTHDAY_FBI_IDX <span class="keyword">ON</span> STUFF(TRUNC(BIRTHDAY));</span><br></pre></td></tr></table></figure>
<p><strong>但是对于MIN、MAX函数等，Oracle仍然会使用索引，因为Oracle对这类聚合分析函数做了相应的优化。</strong></p>
</li>
<li><p>对索引列进行运算导致索引失效</p>
</li>
<li><p>使用前导模糊查询</p>
<p>前导模糊查询的写法是<code>like '%T'</code>，即通配符<code>%</code>写在要匹配的字符前面，这样的情况下不走索引。</p>
</li>
<li><p>where子句中使用不等于条件</p>
<p>不等于操作包括：</p>
<figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line">&lt;&gt;</span><br><span class="line">!=</span><br><span class="line">not col &gt;= ?</span><br><span class="line">not col &lt;= ?</span><br></pre></td></tr></table></figure>
<p>oracle建议，对于这些限制条件可以使用or代替，例如<code>col &lt;&gt; 0</code>可以替换成<code>col &gt; 0 or col &lt; 0</code>。</p>
</li>
<li><p>where子句中使用<code>not in</code>或<code>not exists</code></p>
</li>
<li><p>比较不匹配类型的数据类型</p>
<p>比如sirial_code是一个varchar2类型的字段，在这个字段上建立了索引，但是下面的语句会执行全表扫描而不会走索引。</p>
<figure class="highlight sql"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">SELECT</span> <span class="operator">*</span> <span class="keyword">FROM</span> MATERIALS <span class="keyword">WHERE</span> SERIAL_CODE <span class="operator">=</span> <span class="number">810646874</span>;</span><br></pre></td></tr></table></figure>
</li>
<li><p>表中数据量的多少也会影响索引的使用</p>
<p>如果查询的数量超过大表数量的30%，那就不走索引了。</p>
</li>
</ol>
<h2 id="索引失效的解决办法"><a href="#索引失效的解决办法" class="headerlink" title="索引失效的解决办法"></a>索引失效的解决办法</h2><ul>
<li><p>选用合适的oracle优化器</p>
<p>oracle的优化器有三种，一种是基于规则的（rule），一种是基于成本的（cost），还有一种是选择性的（choose）.</p>
</li>
<li><p>重建索引</p>
</li>
<li><p>强制索引</p>
<p>强制索引是使用hint关键字.</p>
</li>
</ul>

    </div>

    
    
    
        

  <div class="followme">
    <p>欢迎关注我的其它发布渠道</p>

    <div class="social-list">

        <div class="social-item">
          <a target="_blank" class="social-link" href="/atom.xml">
            <span class="icon">
              <i class="fa fa-rss"></i>
            </span>

            <span class="label">RSS</span>
          </a>
        </div>
    </div>
  </div>


      <footer class="post-footer">

        


        
    <div class="post-nav">
      <div class="post-nav-item">
    <a href="/2021/07/26/emacs%E7%94%BB%E5%9B%BE/" rel="prev" title="emacs画图">
      <i class="fa fa-chevron-left"></i> emacs画图
    </a></div>
      <div class="post-nav-item">
    <a href="/2021/07/27/ThreadLocal%E7%B1%BB%E7%9A%84%E4%BD%BF%E7%94%A8/" rel="next" title="ThreadLocal类的使用">
      ThreadLocal类的使用 <i class="fa fa-chevron-right"></i>
    </a></div>
    </div>
      </footer>
    
  </article>
  
  
  



          </div>
          

<script>
  window.addEventListener('tabs:register', () => {
    let { activeClass } = CONFIG.comments;
    if (CONFIG.comments.storage) {
      activeClass = localStorage.getItem('comments_active') || activeClass;
    }
    if (activeClass) {
      let activeTab = document.querySelector(`a[href="#comment-${activeClass}"]`);
      if (activeTab) {
        activeTab.click();
      }
    }
  });
  if (CONFIG.comments.storage) {
    window.addEventListener('tabs:click', event => {
      if (!event.target.matches('.tabs-comment .tab-content .tab-pane')) return;
      let commentClass = event.target.classList[1];
      localStorage.setItem('comments_active', commentClass);
    });
  }
</script>

        </div>
          
  
  <div class="toggle sidebar-toggle">
    <span class="toggle-line toggle-line-first"></span>
    <span class="toggle-line toggle-line-middle"></span>
    <span class="toggle-line toggle-line-last"></span>
  </div>

  <aside class="sidebar">
    <div class="sidebar-inner">

      <ul class="sidebar-nav motion-element">
        <li class="sidebar-nav-toc">
          文章目录
        </li>
        <li class="sidebar-nav-overview">
          站点概览
        </li>
      </ul>

      <!--noindex-->
      <div class="post-toc-wrap sidebar-panel">
          <div class="post-toc motion-element"><ol class="nav"><li class="nav-item nav-level-2"><a class="nav-link" href="#%E5%BC%95%E5%AD%90"><span class="nav-number">1.</span> <span class="nav-text">引子</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#%E5%9C%A8%E5%86%99sql%E7%9A%84%E5%B1%82%E9%9D%A2%E4%B8%8A%EF%BC%8C%E4%B8%80%E4%BA%9B%E5%AF%BC%E8%87%B4%E7%B4%A2%E5%BC%95%E5%A4%B1%E6%95%88%E7%9A%84%E9%AA%9A%E6%93%8D%E4%BD%9C"><span class="nav-number">2.</span> <span class="nav-text">在写sql的层面上，一些导致索引失效的骚操作</span></a></li><li class="nav-item nav-level-2"><a class="nav-link" href="#%E7%B4%A2%E5%BC%95%E5%A4%B1%E6%95%88%E7%9A%84%E8%A7%A3%E5%86%B3%E5%8A%9E%E6%B3%95"><span class="nav-number">3.</span> <span class="nav-text">索引失效的解决办法</span></a></li></ol></div>
      </div>
      <!--/noindex-->

      <div class="site-overview-wrap sidebar-panel">
        <div class="site-author motion-element" itemprop="author" itemscope itemtype="http://schema.org/Person">
  <p class="site-author-name" itemprop="name">田园隐士</p>
  <div class="site-description" itemprop="description">talk is cheap, show me the code</div>
</div>
<div class="site-state-wrap motion-element">
  <nav class="site-state">
      <div class="site-state-item site-state-posts">
          <a href="/archives/">
        
          <span class="site-state-item-count">347</span>
          <span class="site-state-item-name">日志</span>
        </a>
      </div>
      <div class="site-state-item site-state-categories">
            <a href="/categories/">
        <span class="site-state-item-count">53</span>
        <span class="site-state-item-name">分类</span></a>
      </div>
      <div class="site-state-item site-state-tags">
            <a href="/tags/">
        <span class="site-state-item-count">115</span>
        <span class="site-state-item-name">标签</span></a>
      </div>
  </nav>
</div>



      </div>

    </div>
  </aside>
  <div id="sidebar-dimmer"></div>


      </div>
    </main>

    <footer class="footer">
      <div class="footer-inner">
        

        

<div class="copyright">
  
  &copy; 
  <span itemprop="copyrightYear">2022</span>
  <span class="with-love">
    <i class="fa fa-heart"></i>
  </span>
  <span class="author" itemprop="copyrightHolder">田园隐士</span>
    <span class="post-meta-divider">|</span>
    <span class="post-meta-item-icon">
      <i class="fa fa-chart-area"></i>
    </span>
    <span title="站点总字数">587k</span>
    <span class="post-meta-divider">|</span>
    <span class="post-meta-item-icon">
      <i class="fa fa-coffee"></i>
    </span>
    <span title="站点阅读时长">8:53</span>
</div>
  <div class="powered-by">由 <a href="https://hexo.io/" class="theme-link" rel="noopener" target="_blank">Hexo</a> & <a href="https://muse.theme-next.org/" class="theme-link" rel="noopener" target="_blank">NexT.Muse</a> 强力驱动
  </div>

        
<div class="busuanzi-count">
  <script async src="https://busuanzi.ibruce.info/busuanzi/2.3/busuanzi.pure.mini.js"></script>
    <span class="post-meta-item" id="busuanzi_container_site_uv" style="display: none;">
      <span class="post-meta-item-icon">
        <i class="fa fa-user"></i>
      </span>
      <span class="site-uv" title="总访客量">
        <span id="busuanzi_value_site_uv"></span>
      </span>
    </span>
    <span class="post-meta-divider">|</span>
    <span class="post-meta-item" id="busuanzi_container_site_pv" style="display: none;">
      <span class="post-meta-item-icon">
        <i class="fa fa-eye"></i>
      </span>
      <span class="site-pv" title="总访问量">
        <span id="busuanzi_value_site_pv"></span>
      </span>
    </span>
</div>








      </div>
    </footer>
  </div>

  
  <script src="/lib/anime.min.js"></script>
  <script src="/lib/velocity/velocity.min.js"></script>
  <script src="/lib/velocity/velocity.ui.min.js"></script>

<script src="/js/utils.js"></script>

<script src="/js/motion.js"></script>


<script src="/js/schemes/muse.js"></script>


<script src="/js/next-boot.js"></script>




  




  
<script src="/js/local-search.js"></script>













  

  
      

<script>
  if (typeof MathJax === 'undefined') {
    window.MathJax = {
      loader: {
          load: ['[tex]/mhchem'],
        source: {
          '[tex]/amsCd': '[tex]/amscd',
          '[tex]/AMScd': '[tex]/amscd'
        }
      },
      tex: {
        inlineMath: {'[+]': [['$', '$']]},
          packages: {'[+]': ['mhchem']},
        tags: 'ams'
      },
      options: {
        renderActions: {
          findScript: [10, doc => {
            document.querySelectorAll('script[type^="math/tex"]').forEach(node => {
              const display = !!node.type.match(/; *mode=display/);
              const math = new doc.options.MathItem(node.textContent, doc.inputJax[0], display);
              const text = document.createTextNode('');
              node.parentNode.replaceChild(text, node);
              math.start = {node: text, delim: '', n: 0};
              math.end = {node: text, delim: '', n: 0};
              doc.math.push(math);
            });
          }, '', false],
          insertedScript: [200, () => {
            document.querySelectorAll('mjx-container').forEach(node => {
              let target = node.parentNode;
              if (target.nodeName.toLowerCase() === 'li') {
                target.parentNode.classList.add('has-jax');
              }
            });
          }, '', false]
        }
      }
    };
    (function () {
      var script = document.createElement('script');
      script.src = '//cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js';
      script.defer = true;
      document.head.appendChild(script);
    })();
  } else {
    MathJax.startup.document.state(0);
    MathJax.texReset();
    MathJax.typeset();
  }
</script>

    

  

</body>
</html>
